Publications

Published papers

  1. J. Krajczok, P.M. Sołtan: On certain invariants of compact quantum groups. arXiv | DOI
  2. W. Paupa, P.M. Sołtan: Invariants of the quantum graph of the partial trace. arXiv | DOI
  3. J. Krajczok, P.M. Sołtan: Examples of compact quantum groups with \(L^\infty(\mathbb{G})\) a factor. arXiv | DOI
  4. A. Chirvasitu, J. Krajczok, P.M. Sołtan: Compact quantum group structures on type-I \(\mathrm{C}^*\)-algebras. arXiv | DOI
  5. A. Bochniak, P. Kasprzak, P.M. Sołtan: Quantum correlations on quantum spaces. arXiv | DOI
  6. J. Krajczok, P.M. Sołtan: The quantum disk is not a quantum group. arXiv | DOI
  7. P.M. Sołtan: Mathematics and physics of sound and music. Atti dell’Accademia Polacca VIII (2020), 7–15. LINK
  8. P. Kasprzak, P.M. Sołtan: Quantum groups with projection and extensions of locally compact quantum groups. arXiv | DOI
  9. M. Kalantar, P. Kasprzak, A. Skalski, P.M. Sołtan: Induction for locally compact quantum groups revisited. arXiv | DOI
  10. P. Kasprzak, P.M. Sołtan: The Lattice of Idempotent States on a Locally Compact Quantum Group. Publ. arXiv | DOI
  11. P.M. Sołtan: Podleś Spheres for the Braided Quantum \(\mathrm{SU}(2)\). arXiv | DOI
  12. P. Kasprzak, F. Khosravi, P.M. Sołtan: Kawada-Itô-Kelley Theorem for Quantum Semigroups. arXiv | DOI
  13. P.M. Sołtan: Normal idempotent states on a locally compact quantum group. Mathematisches Forschungsinstitut Oberwolfach Report 22 (2018) 1364–1367. LINK | DOI
  14. P.M. Sołtan: Quantum Semigroups from Synchronous Games. arXiv | DOI
  15. J. Krajczok, P.M. Sołtan: Compact quantum groups with representations of bounded degree. J. Operator Th. 80 (2018), 415–428. arXiv | LINK1 | LINK2
  16. K. De Commer, P. Kasprzak, A. Skalski, P.M. Sołtan: Quantum actions on discrete quantum spaces and a generalization of Clifford’s theory of representations. arXiv | DOI
  17. P. Kasprzak, F. Khosravi, P.M. Sołtan: Integrable actions and quantum subgroups. arXiv | DOI
  18. P. Józiak, P. Kasprzak, P.M. Sołtan: Hopf images in locally compact quantum groups. arXiv | DOI
  19. P. Kasprzak, A. Skalski, P.M. Sołtan: The canonical central exact sequence for locally compact quantum groups. arXiv | DOI
  20. U. Franz, A. Skalski, P.M. Sołtan: Introduction to compact and discrete quantum groups. Banach Center Publications 111 (2017), U. Franz, A. Skalski, P.M. Sołtan eds., 9–31. arXiv | DOI
  21. J. Krajczok, P.M. Sołtan: Center of the algebra of functions on the quantum group \(\mathrm{SU}q(2)\) and related topics. arXiv | DOI
  22. A. Skalski, P.M. Sołtan: Quantum families of invertible maps and related problems. arXiv | DOI
  23. P. Kasprzak, P.M. Sołtan: Quantum groups with projection on von Neumann algebra level. arXiv | DOI
  24. P. Kasprzak, P.M. Sołtan, S.L. Woronowicz: Quantum automorphism groups of finite quantum groups are classical. arXiv | DOI
  25. J. Bhowmick, A. Skalski, P.M. Sołtan: Quantum group of automorphisms of a finite quantum group. arXiv | DOI
  26. A. Skalski, P.M. Sołtan: Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras. arXiv | DOI
  27. P. Kasprzak, P.M. Sołtan: Embeddable quantum homogeneous spaces. arXiv | DOI
  28. P.M. Sołtan, A. Viselter: A note on amenability of locally compact quantum groups. arXiv | DOI
  29. P.M. Sołtan: On quantum maps into quantum semigroups. Houston J. Math. 40, No. 3 (2014), 779–790. arXiv | LINK
  30. P.M. Sołtan: Quantum families of maps. The 15th International Workshop for Young Mathematicians “Functional Analysis”, Jagiellonian University, Kraków 2013, pages 107–122. arXiv | LINK
  31. M. Daws, P. Kasprzak, A. Skalski, P.M. Sołtan: Closed quantum subgroups of locally compact quantum groups. arXiv| DOI
  32. T. Banica, A. Skalski, P.M. Sołtan: Noncommutative homogeneous spaces: the matrix case. arXiv | DOI
  33. J. Liszka-Dalecki, P.M. Sołtan: Quantum isometry groups of symmetric groups. arXiv | DOI
  34. D. Kyed, P.M. Sołtan: Property (T) and exotic quantum group norms. arXiv | DOI
  35. P.M. Sołtan: On actions of compact quantum groups. arXiv | DOI
  36. P.M. Sołtan: Examples of non-compact quantum group actions. arXiv | DOI
  37. P.M. Sołtan: When is a quantum space not a group?. Banach Algebras 2009, Banach Center Publications 91 (2010), R.J. Loy, V. Runde, A. Sołtysiak eds., 353–364. arXiv | LINK
  38. P.M. Sołtan: Quantum spaces without group structure. Proc. Amer. Math. Soc. 138 (2010), 2079–2086. arXiv | DOI
  39. P.M. Sołtan: Quantum \(\mathrm{SO}(3)\) groups and quantum group actions on \(M_2\). J. Noncommut. Geom. 4 (2010), 2–28. arXiv | DOI
  40. P.M. Sołtan: On quantum semigroup actions on finite quantum spaces. Infin. Dimens. Anal. Quantum. Probab. Relat. Top. 12 no. 3 (2009), 503–509. arXiv | DOI
  41. P.M. Sołtan: Quantum families of maps and quantum semigroups on finite quantum spaces. J. Geom. Phys. 59 (2009) 354–368. arXiv | DOI
  42. P.M. Sołtan: Examples of quantum commutants. “Interactions of Algebraic & Coalgebraic Structures (Theory and Applications)”, Arab J. Sci. Eng. 33 no. 2C (2008), 447–457. arXiv
  43. P.M. Sołtan, S.L. Woronowcz: From multiplicative unitaries to quantum groups II. arXiv | DOI
  44. P.M. Sołtan: Compactifications of discrete quantum groups. arXiv | DOI
  45. P.M. Sołtan: Quantum Bohr compactification. arXiv | DOI
  46. P.M. Sołtan: New quantum “\(az+b\)” groups. arXiv | DOI
  47. W. Pusz, P.M. Sołtan: Functional form of unitary representations of the quantum “\(az+b\)” group. arXiv | DOI
  48. P.M. Sołtan, S.L. Woronowcz: A remark on manageable multiplicative unitaries. arXiv | DOI
  49. P.M. Sołtan: A remark on the spectrum of the analytic generator. arXiv | DOI

Preprints

  1. J. Krajczok, P.M. Sołtan: Braided quantum \(\mathrm{SU}(2)\) group - a case study arXiv
  2. A. Chirvasitu, P.M. Sołtan, M. Wasilewski: Quantum-rigid random quantum graphs arXiv
  3. A. Bochniak, I. Chełstowski, P. Kasprzak, P.M. Sołtan: Quantum Mycielskians: symmetries, twin vertices and distinguishing labelings arXiv

Notes in English

  1. Groups, algebras and means LINK
  2. Uniqueness of the hyperfinite II_1 factor LINK
  3. Amenability and exactness for group actions and operator algebras LINK
  4. Affine isometric actions on Hilbert spaces and amenability LINK
  5. \(\mathrm{C}^*\)-algebras, group actions and crossed products (lecture notes) LINK
  6. A survey of quantum \(az+b\) groups. LINK

Notes in Polish

  1. Prostota \(\mathrm{C}^*_r(\mathbb{F}_2)\) LINK
  2. Twierdzenie o imprymitywności LINK
  3. Teoria Tomity-Takesakiego LINK
  4. Twierdzenie Kreina-Smuliana LINK
  5. Minimalne działanie grupy \(\mathrm{SU}_q(N)\) na pełnym faktorze - notatki z pracy Y. Uedy LINK
  6. Geometryczna teoria grup LINK
  7. Reprezentacje indukowane i teoria Mackeya LINK

Books

Other

  • P.M. Sołtan: Laudatio for Professor S.L. Woronowicz recipient of the Wigner medal 2024. In “Geometric methods in physics XLII”, Trends Math. (2026), 15-17. DOI | LINK
  • W. Pusz, P.M. Sołtan: On some low dimensional quantum groups. arXiv
  • W. Pusz, P.M. Sołtan: Analysis on a homogeneous space of a quantum group. arXiv